The semi-analytical modeling and vibration reduction analysis of the cylindrical shell with piezoelectric shunt damping patches

By considering electromechanical coupling, a unified dynamic model of the cylindrical shell with the piezoelectric shunt damping patch(PSDP) is created. The model is universal and can simulate the vibration characteristic of the shell under different states including the states in which PSDP cannot be connected, partially connected, and completely connected to the shunt circuit. The equivalent loss factor and elastic modulus with frequency dependence are proposed to consider the electrical damping effect of resistance shunt circuits. Moreover, the semi-analytical dynamic equation of the cylindrical shell with PSDP is derived by the Lagrange equation. An experimental test is carried out on the cylindrical shell with PSDP to verify the vibration suppression ability of PSDP on the cylindrical shell and the correctness of the proposed model. Furthermore, the parameter analysis shows that determining the appropriate resistance value in the shunt circuit can achieve a good vibration suppression effect.

Wave propagation in beams with anti-symmetric piezoelectric shunting arrays

Piezoelectric shunting arrays are employed to control the wave propagation in flexible beams. Contrary to conven- tional symmetric configuration, a substrate beam with anti-symmetric shunting arrays is investigated by adapted transfer matrix method. Compared with symmetric scheme, the anti-symmetric one demonstrates some distinctive characteristics. Primarily, the longitudinal and fiexural waves are coupled, so they are correlated and must be considered simultaneously. Moreover, the attenuation of flexural wave is much stronger in anti-symmetric scenario, while the longitudinal wave demon- strates the converse side. As a result, the anti-symmetric scheme can be utilized to improve the vibration isolation capability of shunting arrays. Finally, the theoretical analyses are validated by finite element simulations.

Tunable band gaps in acoustic metamaterials with periodic arrays of resonant shunted piezos

Periodic arrays of resonant shunted piezoelectric patches are employed to control the wave propagation in a two-dimensional （2D） acoustic metamaterial. The performance is characterized by the finite element method. More importantly, we propose an approach to solving the conventional issue of the nonlinear eigenvalue problem, and give a convenient solution to the dispersion properties of 2D metamaterials with periodic arrays of resonant shunts in this article. Based on this modeling method, the dispersion relations of a 2D metamaterial with periodic arrays of resonant shunted piezos are calculated. The results show that the internal resonances of the shunting system split the dispersion curves, thereby forming a locally resonant band gap. However, unlike the conventional locally resonant gap, the vibrations in this locally resonant gap are unable to be completely localized in oscillators consisting of shunting inductors and piezo-patches.

Band gap structure analysis of phononic crystal rods with hybrid shunted piezoelectric patches

The band gap structures by arranging hybrid shunted piezoelectric materialswith resistance inductive （RL） circuit and negative impedance converter （NIC） closely and at in- tervals are presented. The theoretical model is built using transfer matrix method. Then the MATLAB computing language is utilized to simulate the band gap structures. Meanwhile, the effects of the resistance, inductance and capacitance on the local resonant gap are studied. By comparing different combinations of resistance, inductance and capacitance as well as different arrangement of circuits, a 13 kHz band gap is reached under the effect of arranging hybrid pe- riodic shunted piezoelectric patches at intervals and the stability of the system is also analyzed. It is proved that utilizing hybrid shunted piezoelectric patches would have a clear impact on the band gap structure of phononic crystal rods. Moreover, the band gap would be clearly enlarged by arranging hybrid piezoelectric patches at intervals.

Enhanced wave and finite element method for wave propagation and forced response prediction in periodic piezoelectric structures

As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers;the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials（PZT）. Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative.

Two Kinds Equal Frequency Circuits to Achieve Locally Resonant Band Gap of a Circular Plate Attached Alternately by Piezoelectric Unimorphs

A circular thin plate is proposed for vibration attenuation,which is attached alternately by annular piezoelectric unimorphs with resonant shunt circuits.Two kinds of equal frequency resonant shunt circuits are designed to achieve an integrated locally resonant（LR）band gap（BG） with a much smaller transmission factor：（1） the structure is arrayed periodically while the resonant shunt circuits are aperiodic;（2） the resonant shunt circuits are periodic while the structure is aperiodic.The transmission factor curve is calculated,which is validated by the finite element method.Dependences of the LR BG performance upon the geometric and electric parameters are also analyzed.